The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems （RDS）, which can be generated by solutions of some stochastic partial differential equations on...The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems （RDS）, which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.展开更多
This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrodinger equations with homogeneous Dirichlet boundary condition.The authors prove the existence of compact ...This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrodinger equations with homogeneous Dirichlet boundary condition.The authors prove the existence of compact kernel sections for the associated process by using a suitable decomposition of the equations.展开更多
The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to pr...The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to prove the existence of the pullback attractor for the 2D g-Navier-Stokes eauations is given.展开更多
The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved i...The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .展开更多
In this paper, we consider a non-autonomous model for epitaxial growth. It is shown that a pullback attractor of the model exists when the external force has exponential growth.
This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1...This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1</sup>(R<sup>n</sup>). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise.展开更多
In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semi...In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semigroup and the existence of the global展开更多
In this paper, we study the existence of global attractor of a class of three-dimensional Brinkman-Forchheimer equation in some unbounded domains which satisfies Poincaré inequality. We use the tail estimation me...In this paper, we study the existence of global attractor of a class of three-dimensional Brinkman-Forchheimer equation in some unbounded domains which satisfies Poincaré inequality. We use the tail estimation method to establish the asymptotic compactness of the solution operator and then prove the existence of the global attractor in(H_0~1(Ω))~3.展开更多
The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(R^(n))×L^(2)(R^...The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(R^(n))×L^(2)(R^(n))and attracts all tempered random sets of L^(2)(R^(n))×L^(2)(R^(n))in the topology of Hs(R^(n))×L^(2)(R^(n))with s∈(0,1).By the idea of positive and negative truncations,spectral decomposition in bounded domains,and tail estimates,we achieved the desired results.展开更多
The long time behavior of the solutions of some partly dissipative reaction diffusion systems is studied. We prove the existence of a compact （L^2 × L^2 - H^1 × L^2） attractor for a partly dissipative reac...The long time behavior of the solutions of some partly dissipative reaction diffusion systems is studied. We prove the existence of a compact （L^2 × L^2 - H^1 × L^2） attractor for a partly dissipative reaction diffusion system in Rn. This improves a previous result obtained by A. Rodrigues-Bernal and B. Wang concerning the existence of a compact （L^2 × L^2 - L^2 × L^2） attractor for the same system.展开更多
基金the National NSFC under grant No.50579022the Foundation of Pre-973 Program of China under grant No.2004CCA02500+1 种基金the SRF for the ROCS,SEMthe Talent Recruitment Foundation of HUST
文摘The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems （RDS）, which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.
基金the NNSFC(10771139 and 10771074)NSF of Wenzhou University(2007L024)NSF of Guangdong Province(004020077)
文摘This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrodinger equations with homogeneous Dirichlet boundary condition.The authors prove the existence of compact kernel sections for the associated process by using a suitable decomposition of the equations.
基金Project supported by the National Natural Science Foundation of China (No. 10871156)the Fund of Xi’an Jiaotong University (No. 2009xjtujc30)
文摘The existence of the pullback attractor for the 2D non-autonomous g-Navier- Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to prove the existence of the pullback attractor for the 2D g-Navier-Stokes eauations is given.
文摘The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .
基金The NSF(11401258)of Chinathe NSF(BK20140130)of Jiangsu Province
文摘In this paper, we consider a non-autonomous model for epitaxial growth. It is shown that a pullback attractor of the model exists when the external force has exponential growth.
文摘This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1</sup>(R<sup>n</sup>). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise.
基金Supported by the NNSF of China(11031003,11271066)Supported by the Shanghai Education Commission(13ZZ048)
文摘In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semigroup and the existence of the global
基金Supported by the National Natural Science Foundation of China (12001420)。
文摘In this paper, we study the existence of global attractor of a class of three-dimensional Brinkman-Forchheimer equation in some unbounded domains which satisfies Poincaré inequality. We use the tail estimation method to establish the asymptotic compactness of the solution operator and then prove the existence of the global attractor in(H_0~1(Ω))~3.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.11771444,11871138)the Yue Qi Young Scholar Project+3 种基金China University of Mining and Technology(Beijing),China Scholarship Council(CSC)the Funding of V.C.&V.R.Key Lab of Sichuan Provincethe Funding of Young Backbone Teacher in Henan ProvinceHenan Overseas Expertise Introduction Center for Discipline Innovation.
文摘The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(R^(n))×L^(2)(R^(n))and attracts all tempered random sets of L^(2)(R^(n))×L^(2)(R^(n))in the topology of Hs(R^(n))×L^(2)(R^(n))with s∈(0,1).By the idea of positive and negative truncations,spectral decomposition in bounded domains,and tail estimates,we achieved the desired results.
基金Supported by the Key Teachers Foundation of Chongqing University(No.2003018)the Key Teachers Foundation of Universities in Chongqing(No.20020126).
文摘The long time behavior of the solutions of some partly dissipative reaction diffusion systems is studied. We prove the existence of a compact （L^2 × L^2 - H^1 × L^2） attractor for a partly dissipative reaction diffusion system in Rn. This improves a previous result obtained by A. Rodrigues-Bernal and B. Wang concerning the existence of a compact （L^2 × L^2 - L^2 × L^2） attractor for the same system.
